An open-loop error identification method for a hemispherical resonator gyro

Abstract

The application discloses a kind of open loop hemispherical resonator gyro error identification methods, the vibration energy of the resonator mainly collected as the input of algorithm, and after following processing: 1) by tracking differentiator reduces initial error, effectively solve the contradiction of overshoot and rapidity, reduce external compensation energy, reduce drive voltage consumption;2) by extended state observer to track the variable trend of hemispherical gyro in real time, the degree of dependence on model is low;3) by nonlinear state error feedback control law to eliminate noise strong and robustness strong anti-interference.Solve the technical problems that prior art exists system stability, control precision is not high.

Description

Technical Field

[0001] This invention belongs to the field of hemispherical resonant gyroscopes, and in particular, it designs an error identification method for open-loop hemispherical resonant gyroscopes. Background Technology

[0002] The hemispherical resonator gyroscope is a promising new type of high-precision Coriolis vibration gyroscope. It is one of the most promising sensitive devices in strapdown inertial differential systems for aerospace vehicles. It features high precision and long lifespan and will be widely used in various fields such as weaponry, aviation, and aerospace. In particular, it is undoubtedly the best choice for space applications such as environmental satellites, communication satellites, space stations, lunar exploration, space telescopes, and deep space exploration, and will have broad application prospects.

[0003] However, since a hemispherical resonant gyroscope consists of two parts: a sensing element and a circuit, its error sources include errors in both the sensing element and the circuit. The main error sources include:

[0004] 1) Errors in the hemispherical resonant gyroscope caused by base vibration;

[0005] 2) Errors caused by the resonant frequency drift of the harmonic oscillator;

[0006] 3) The harmonic oscillator is circumferentially asymmetrical;

[0007] 4) The harmonic oscillator and the signal detector are not concentric;

[0008] 5) Errors caused by the fourth and second harmonics due to the uneven mass distribution of the harmonic oscillator;

[0009] 6) Errors in the hemispherical resonator gyroscope caused by inconsistent quality factors of the harmonic oscillator;

[0010] 7) Errors caused by uneven circumferential distribution and unequal gain of the exciter;

[0011] 8) Errors caused by uneven circumferential distribution, misalignment, and unequal gain of the vibration pickups;

[0012] 9) Due to the phase difference between the output axes of the X and Y electrodes;

[0013] 10) Noise in the output signals of the X and Y electrodes;

[0014] 11) Asymmetrical damping causes the resonant frequencies of the output shafts of the X and Y electrodes to be unequal;

[0015] 12) Errors caused by environmental factors such as temperature, air pressure, humidity, radiation, and sunlight.

[0016] These errors are all deterministic systematic errors. The random errors of a hemispherical resonator gyroscope are mainly due to instabilities in the electronic circuitry and gyroscope structure, instabilities in the excitation voltage, instabilities in the signal acquisition and processing system, 1 / f noise caused by random fluctuations in the electrical differential, shot noise, and burst noise.

[0017] The error of the hemispherical resonator gyroscope is one of the main error sources of inertial systems. The operating accuracy of an inertial differential navigation system largely depends on the operating accuracy of the hemispherical resonator gyroscope. Imperfections in the structure of the hemispherical resonator gyroscope itself, the influence of certain physical factors, and the motion of the object being used can all generate interference torques and cause errors, thus affecting the operating accuracy of the hemispherical resonator gyroscope.

[0018] Existing methods for temperature drift compensation of hemispherical resonant gyroscopes based on resonant frequency, construction forms and filtering methods for attitude measurement systems based on HRG and star sensors, and compensation methods for BP neural networks optimized by genetic algorithms still suffer from technical problems. These problems include the inaccurate error control of hemispherical resonant gyroscopes based on empirically setting relevant gyroscope parameters, which affects the working accuracy of the hemispherical resonant gyroscopes.

[0019] To address the aforementioned technical issues, a novel method for identifying open-loop hemispherical resonant gyroscope errors needs to be proposed to improve the accuracy of gyroscope error identification and control. Summary of the Invention

[0020] The purpose of this invention is to provide an error identification method for open-loop hemispherical resonant gyroscopes (HRGs). In open-loop HRG control, it mainly employs PSO (Programmable Optimization) technology to intelligently adjust the parameters of the active disturbance rejection control (AOC) algorithm. Furthermore, a Pareto optimal strategy is introduced into the PSO to intervene in the particle swarm position iteration process, maintaining the diversity of the particle swarm. This control optimization strategy ensures the control accuracy and output accuracy of the system. System error compensation is achieved by updating the preset disturbance value of the extended state observer. Finally, by solving the matrix equation, all errors within the consideration range generated during machine tool processing are accurately identified, providing an effective error compensation basis for the design of force balance and full-angle HRG control systems. This solves the technical problem that setting gyroscope parameters based on empirical methods results in inaccurate error control of the hemispherical resonant gyroscope, affecting its working accuracy.

[0021] The present invention adopts the following technical solution:

[0022] Embodiment 1 of the present invention provides a method for identifying errors in an open-loop hemispherical resonant gyroscope, comprising:

[0023] Calculate the first-order and second-order nonlinear state errors of the harmonic oscillator amplitude of the gyroscope, respectively;

[0024] The first response function is determined based on the first-order nonlinear state error;

[0025] The second response function is determined based on the second-order nonlinear state error;

[0026] The first coefficient of the first response function and the second coefficient of the second response function were obtained by using the particle swarm optimization algorithm.

[0027] Finally, the control force of the gyroscope is determined based on the first response function, the second response function, the first coefficient, and the second coefficient.

[0028] Optionally, the calculation of the first-order nonlinear state error and the second-order nonlinear state error of the gyroscope's harmonic oscillator amplitude includes:

[0029] The first-order state estimate of the gyroscope's harmonic oscillator amplitude is obtained by weighted calculation using the extended state system based on the extended state error, the third coefficient of the extended state error, the first derivative of the gyroscope's harmonic oscillator amplitude, and the second derivative of the harmonic oscillator amplitude.

[0030] The difference between the first-order state estimate and the first preset state fitting value is calculated to obtain the first-order nonlinear state error.

[0031] Optionally, the calculation of the first-order nonlinear state error and the second-order nonlinear state error of the gyroscope's harmonic oscillator amplitude includes:

[0032] Based on the extended state error, the first extended state response function corresponding to the state error, the fourth coefficient of the first extended state response function, the second derivative of the gyroscope's harmonic oscillator amplitude, and the third derivative of the harmonic oscillator amplitude are weighted and calculated through the extended state system to obtain the second-order state estimate of the gyroscope's harmonic oscillator amplitude.

[0033] The second-order nonlinear state error is obtained by subtracting the second-order state estimate of the harmonic oscillator amplitude from the fitted value of the second preset state.

[0034] Optionally, the extended state error can be calculated as follows:

[0035] The expansion state error is obtained by calculating the difference between the first derivative of the harmonic oscillator amplitude and the preset harmonic oscillator amplitude.

[0036] Optionally, the first-order differential is calculated by differentiating the amplitude of the harmonic oscillator of the gyroscope using a tracking differentiator to obtain the first-order differential of the harmonic oscillator amplitude.

[0037] Optionally, determining the first response function based on the first-order nonlinear state error includes:

[0038] The first-order nonlinear state error is used as the input to the preset step response function to determine the first response function.

[0039] Optionally, determining the second response function based on the second-order nonlinear state error includes:

[0040] The second-order nonlinear state error is used as the input to the preset step response function to determine the second response function.

[0041] Optionally, the first coefficient of the first response function and the second coefficient of the second response function can be solved using a particle swarm optimization algorithm.

[0042] Optionally, the method further includes:

[0043] The second expansion state response function is calculated based on the expansion state error in the above embodiments;

[0044] The third-order state estimate of the harmonic oscillator amplitude is obtained by weighting the third-order derivative of the gyroscope's harmonic oscillator amplitude and the second extended state response function through the extended state system.

[0045] Calculate the difference between the control force of the gyroscope and the third-order state estimate;

[0046] The total disturbance value of the system is obtained by further calculating the ratio of the difference to the preset value;

[0047] By updating the preset disturbance of the expanded state system with the obtained total disturbance, system error compensation is achieved.

[0048] The beneficial effects of this invention are as follows: In open-loop HRG control, this algorithm mainly employs PSO technology to intelligently adjust the parameters of the active disturbance rejection control algorithm. Furthermore, the Pareto optimal strategy is introduced into PSO to intervene in the particle swarm position iteration process, maintaining the diversity of the particle swarm. This control optimization strategy ensures the control accuracy and output accuracy of the system. By updating the preset disturbance value of the extended state observer, system error compensation is achieved, further improving the system's control accuracy. Finally, by solving the matrix equations, all errors within the consideration range generated during machine tool processing are accurately identified, providing an effective error compensation basis for the design of force balance and full-angle HRG control systems. Attached Figure Description

[0049] Figure 1 This is a schematic diagram of the steps of an open-loop hemispherical resonant gyroscope error identification method provided in Embodiment 1 of the present invention;

[0050] Figure 2 This is a schematic diagram of a hemispherical resonant gyroscope control optimization process provided in Embodiment 1 of the present invention;

[0051] Figure 3 This is a schematic diagram of the steps of a dual-objective particle swarm optimization method provided in Embodiment 1 of the present invention;

[0052] Figure 4 This is a schematic diagram illustrating the implementation steps of a particle swarm algorithm according to Embodiment 1 of the present invention. Detailed Implementation

[0053] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0054] Combination Figure 1 and Figure 2 Embodiment 1 of the present invention provides a method for identifying errors in an open-loop hemispherical resonant gyroscope, comprising:

[0055] Step S101: Calculate the first-order nonlinear state error and the second-order nonlinear state error of the gyroscope's harmonic oscillator amplitude, respectively;

[0056] In one embodiment, the present application utilizes the tracking differentiator, extended state observer, and nonlinear state error feedback control law in ADRC to maintain the amplitude of the harmonic oscillator of the hemispherical resonant gyroscope to a constant value. The detection gyroscope electrode picks up the vibration energy output by the electrode, demodulates the vibration energy, and then processes it using the algorithm provided by the present invention. Finally, the driving voltage is used to generate the excitation electrode of the gyroscope, forming the control force for controlling the gyroscope.

[0057] Therefore, in the design process of the nonlinear state error feedback control law, the actual control force of the gyroscope is calculated on the one hand, and the total disturbance of the system is estimated on the other hand. Compensation is carried out in the design process of the nonlinear state error feedback control law to achieve the function of active anti-interference.

[0058] Therefore, the input signal of the ADRC algorithm in this application is specifically the harmonic oscillator amplitude of the fourth harmonic of the gyroscope. By performing first-order, second-order, and third-order differentials on the harmonic oscillator amplitude of the fourth harmonic of the gyroscope respectively, the physical mechanism causing the error is analyzed, the error mathematical model is obtained through mathematical derivation, and the relevant parameters in the model are determined by the data measured in the experiment.

[0059] In the design of nonlinear state error feedback control law, the third derivative can be regarded as the total disturbance of the system. Therefore, the control force of the gyroscope is mainly determined by the first and second derivatives of the harmonic oscillator amplitude and their estimation.

[0060] Specifically, the first-order nonlinear state error of the gyroscope's harmonic oscillator amplitude is calculated by weighting the extended state error, the third coefficient of the extended state error, the first derivative of the gyroscope's harmonic oscillator amplitude, and the second derivative of the harmonic oscillator amplitude through the extended state system to obtain the first-order state estimate of the gyroscope's harmonic oscillator amplitude.

[0061] The difference between the first-order state estimate and the first preset state fitting value is calculated to obtain the first-order nonlinear state error.

[0062] In one specific embodiment, the first-order nonlinear state error is calculated as shown in formula (1):

[0063] Optionally, the extended state error can be calculated as follows:

[0064] The expansion state error is obtained by calculating the difference between the first derivative of the harmonic oscillator amplitude and the preset harmonic oscillator amplitude.

[0065] e = z1(k) - E(k),

[0066] z1(k+1)=z1(k)+h·[z2(k)]-β 01 ·e],

[0067] e1 = x d1 (k+1)-z1(k+1),, (1)

[0068] Where e is the extended state error, E(k) is the preset harmonic oscillator amplitude in the extended state observer, and z 1(k) The first derivative of the fourth harmonic oscillator amplitude of the gyroscope is z2(k), the second derivative of the harmonic oscillator amplitude is z2(k), and β is β. 01 The third coefficient is the extended state error, z1(k+1) is the first-order state estimate of the harmonic oscillator amplitude, and x is the third coefficient. d1 (k+1) is the first preset state fitting value in the tracking differentiator, and e1 is the first-order nonlinear state error.

[0069] Based on the extended state error, the first extended state response function corresponding to the state error, the fourth coefficient of the first extended state response function, the second derivative of the gyroscope's harmonic oscillator amplitude, and the third derivative of the harmonic oscillator amplitude are weighted and calculated through the extended state system to obtain the second-order state estimate of the gyroscope's harmonic oscillator amplitude.

[0070] The second-order nonlinear state error is obtained by subtracting the second-order state estimate of the harmonic oscillator amplitude from the fitted value of the second preset state.

[0071] In a specific embodiment, the second-order nonlinear state error is similarly calculated as shown in formula (2):

[0072] z2(k+1)=z2(k)+h·[z3(k)-β 02 ·f2(e, α1, δ)+b0·f E (k)],

[0073] e2=x d2 (k+1)-z2(k+1), (2)

[0074] Where e is the extended state error, z2(k) is the second derivative of the amplitude of the fourth harmonic oscillator of the gyroscope, z3(k) is the third derivative of the amplitude of the fourth harmonic oscillator of the gyroscope, f2(e, α1δ) is the first extended state response function corresponding to the state error, and β 02 Here, f is the fourth coefficient of the first extended state response function, h is a known constant, b0 refers to the gain of the active disturbance rejection controller output control voltage, which is generally set to 1, and f E (k) represents the system's preset total disturbance, z2(k+1) is the second-order state estimate of the harmonic oscillator amplitude, and x d2 (k+1) is the second preset state fitting value in the tracking differentiator, and e2 is the second-order nonlinear state error.

[0075] Step S102: Determine the first response function based on the first-order nonlinear state error;

[0076] Optionally, determining the first response function based on the first-order nonlinear state error includes:

[0077] The first-order nonlinear state error is used as the input to the preset step response function to determine the first response function.

[0078] In one embodiment, a preset saving response function is provided, as shown in formula (3):

[0079]

[0080] Using e1 as the input to the preset saving response function, we obtain f2(e1, α1, δ), which is the first response function.

[0081] Step S103: Determine the second response function based on the second-order nonlinear state error;

[0082] Optionally, determining the second response function based on the second-order nonlinear state error includes:

[0083] The second-order nonlinear state error is used as the input to the preset step response function to determine the second response function.

[0084] In one embodiment, e2 is similarly used as the input to the preset saving response function described by formula (3) to obtain f2(e2, α2, δ), which is the second response function.

[0085] Step S104: Solve for the first coefficient of the first response function and the second coefficient of the second response function using the particle swarm optimization algorithm.

[0086] In one embodiment, combined with Figure 4The particle swarm optimization algorithm is used to optimize the first coefficient of the first response function and the second coefficient of the second response function by using the error performance index obtained through real-time feedback.

[0087] In one embodiment, the technical solution of this application optimizes the main parameters of ADRC using the principle of separation. First, it optimizes β in the extended state observer. 01 ,β 02 and β 03 PSO processing is performed using a single-objective function optimization strategy. The objective function for this process is:

[0088] Where J1 represents the minimum value of the total expansion state error.

[0089] Next, PSO processing is performed on β1 and β2 in the nonlinear state error feedback control law, using a dual-objective function optimization strategy. Here, β1 is the first coefficient of the first response function, and β2 is the second coefficient of the second response function. The first objective function corresponding to the first coefficient is: Where J2 represents the minimum first-order nonlinear state error and the second objective function corresponding to the second coefficient: Where J3 represents the minimum value of the second-order nonlinear state error.

[0090] It should be noted that this optimization process belongs to multi-objective particle swarm optimization. First, a leader particle needs to be selected to lead the entire swarm rapidly towards the Pareto front; this is the optimal particle selection strategy. Second, to ensure the particle swarm's optimization process has strong momentum from start to finish, the selection of the inertia weight *w* and the number of particles or iterations must be designed, while maintaining the hybridization characteristics during the iteration process. This ensures that the particle swarm does not get trapped in local optima.

[0091] Specifically, in the PSO process, an adaptive function is first designed as shown in formula (4).

[0092]

[0093]

[0094] in, and It refers to the speed of the current generation of particles and the speed of the next generation of particles. and This refers to the position of the current generation of particles and the position of the next generation of particles. Particle velocity and position are used for the optimal position of the current particle and the position of the globally optimal particle.

[0095] As shown in formula (5), the objective function is selected as:

[0096]

[0097] Taking the first particle as the number and the second particle as the coefficient, the coordinates (β1, β2) are the positions of the particles. The optimization of β1 and β2 is reflected in the search for the optimal position of the particle swarm during the process of minimizing the objective function.

[0098] Optionally, such as Figure 3 As shown, a specific particle swarm optimization algorithm for solving for the first coefficient of the first response function and the second coefficient of the second response function includes the following steps:

[0099] Step 1: Determine the upper and lower boundaries of the first and second coefficients to be optimized, as well as the optimization region;

[0100] Step 2: Calculate the first objective function value corresponding to the current particle position of the first coefficient and the second objective function value corresponding to the current particle position of the second coefficient, and store the historical best position of each particle and the global best position of all particles;

[0101] Step 3: Determine whether the distance between the global optimal positions corresponding to the two objective functions is greater than 0.1. If it is, proceed to step 4; otherwise, jump to step 5.

[0102] Step 4: Activate the Pareto optimal strategy to intervene in the position of the current particle swarm after at least 5 iterations. Specifically, the position of a portion of the better particles corresponding to the first objective function is swapped with the same number of better particles corresponding to the second objective function.

[0103] Step 5: Determine whether the global optimal position in the first 5 generations corresponding to the first objective function or the second objective function has been updated at least once. If so, proceed to step 7; otherwise, execute step 6.

[0104] Step 6: Randomly select some particles from the particle swarm corresponding to the first objective function and the particle swarm corresponding to the second objective function, respectively, and hybridize the historical best position of these particles with their current position to generate new particles;

[0105] Step 7: Update the fitness function value of each particle corresponding to the first objective function and the second objective function; perform two-point-one-line hybridization on the particle positions corresponding to the dual objective functions according to the random hybridization strategy;

[0106] Step 8: Determine if the global optimal position is the same in the first 10 generations. If so, proceed to step 9; otherwise, go back to step 2.

[0107] Step 9: After the particle swarm optimization algorithm is completed, the Pareto optimal solution set is obtained by inductive reasoning through the fitness function. The two objective function values ​​in the solution set are plotted on a two-dimensional coordinate system as horizontal and vertical coordinates, respectively, to determine the first coefficient of global optimum corresponding to the first objective function and the second coefficient of global optimum corresponding to the second objective function.

[0108] A specific implementation step of the particle swarm optimization algorithm is as follows: Figure 4 As shown, 1) Initialize the particle swarm position and velocity; 2) Select the individual historical optimum and global optimum according to the fitness function; 3) Calculate the fitness value; 4) Update the particle swarm position and velocity; 5) Determine if the particle objective function value is better than pbest; if not, proceed to step 6); if yes, assign the particle information to pbest, further determine if the objective function value is better than pbest, if yes, proceed to step 6) determine if the global optimum value of the particle swarm remains unchanged for 5 consecutive generations, if not, update the fitness function value of each particle corresponding to the dual objective function, and proceed to step 7); if yes, randomly select some particles, hybridize the historical optimum position of these particles with the current position of these particles to generate new particles, and proceed to step 7) determine if the global optimum value of the particle swarm remains unchanged for 10 consecutive generations, if not, return to step 4) to continue iterating; if yes, obtain the Pareto optimal solution set and determine the global non-dominated solution of the final dual objective problem.

[0109] Step S105: Finally, determine the control force of the gyroscope based on the first response function, the second response function, the first coefficient, and the second coefficient.

[0110] In one embodiment, the control force of the gyroscope is output by weighting the first response function, the second response function, the first coefficient, and the second coefficient according to the calculation method of the following formula (6).

[0111] u0(k+1)=β1·f2(e1, α1, δ)+β2·f2(e2, α2, δ), (6)

[0112] Where f2(e1, α1, δ) is the first response function, f2(e2, α2, δ) is the second response function, β1 is the first coefficient of the first response function, β2 is the second coefficient of the second response function, and u0(k+1) is the force exerted by the system output on the gyroscope.

[0113] Optionally, the first derivative is calculated by differentiating the amplitude of the harmonic oscillator of the gyroscope using a tracking differentiator to obtain the first derivative of the harmonic oscillator amplitude.

[0114] In one embodiment, before performing steps S101-S105, the amplitude of the fourth harmonic of the gyroscope is selected and differentiated using a differential tracker to obtain the first derivative of the gyroscope amplitude. The function of the tracking differentiator is to output the first preset state fitting value x of the vibration energy. d1 (k+1) and its first derivative second preset state fitting value x d2 (k+1) is fed into the input signal of the nonlinear feedback control law, by delaying x d1 (k+1) and x d2 The change rate of (k+1) is used to reduce the overshoot in the control process, thereby enabling the gyroscope to transition from an unworking state to a steady state, reducing the initial error, reducing the impact on the system in the initial stage, and effectively solving the contradiction between overshoot and speed.

[0115] Optionally, the method further includes:

[0116] The second expansion state response function is calculated based on the expansion state error in the above embodiments;

[0117] The third-order state estimate of the harmonic oscillator amplitude is obtained by weighting the third-order derivative of the gyroscope's harmonic oscillator amplitude and the second extended state response function through the extended state system.

[0118] Calculate the difference between the control force of the gyroscope and the third-order state estimate;

[0119] The total disturbance value of the system is obtained by further calculating the ratio of the difference to the preset value;

[0120] By updating the preset disturbance of the expanded state system with the obtained total disturbance, system error compensation is achieved.

[0121] In one embodiment, the following calculation is performed in conjunction with formula (7):

[0122] z3(k+1)=z3(k)+h·[-β 03 ·f2(c, α2, δ)],

[0123]

[0124] Where f2(e, α2, δ) is the response function of the second extended state, and z3(k) is the third derivative of the harmonic oscillator amplitude; z3( k+1 The third-order state estimate of the harmonic oscillator amplitude; u0(k+1)-z3(k+1) is the difference between the control force of the gyroscope and the third-order state estimate; f E (k+1) represents the total disturbance value of the system.

[0125] It should be noted that the method provided in this application first considers practical factors such as the inherent resonance properties of the hemispherical resonant gyroscope, the unavoidable noise input of the detection drive, the errors in the manufacturing process, and the limitations of modeling. Therefore, an active disturbance rejection controller (ADRC) is chosen to replace the traditional PID controller. The ADRC includes a tracking differentiator, an extended state observer, and a nonlinear state error feedback control law. In the first stage of this embodiment, the ADRC algorithm is used to process the fourth harmonic signal of the acquired gyroscope. First, the differentiator tracker can obtain the first derivative of the harmonic oscillator amplitude based on the input gyroscope's harmonic oscillator amplitude, and can also obtain the second and third derivatives of the harmonic oscillator amplitude through an internal iterative algorithm. Second, the first, second, and third derivatives of the harmonic oscillator amplitude obtained by the differentiator tracker are used as inputs to the extended state observer, and observation is performed in conjunction with the preset total disturbance in the extended state observer. The estimation process yields estimates of the first, second, and third derivatives of the harmonic oscillator amplitude, with the first derivative estimate being the primary state variable of the system output. Finally, during the design of the nonlinear state error feedback control law, the first and second nonlinear state errors are calculated based on the first and second derivative estimates of the harmonic oscillator amplitude. The corresponding first and second response functions, along with the first and second coefficients, are then weighted to obtain the gyroscope's control force. Furthermore, the total disturbance of the system is estimated based on the third derivative, used to update the preset disturbance in the extended state observer, thereby compensating for the total system disturbance and improving the accuracy of the system output control force acting on the gyroscope. In the second stage, a particle swarm optimization algorithm is used to optimize the key parameters of each stage of the tracking differentiator, extended state observer, and nonlinear state error feedback control law based on error indices, improving the system's output accuracy. Compared to traditional PID controllers, active disturbance rejection controllers (ADRCs) offer the following advantages: 1) They reduce initial error by using a tracking differentiator, effectively resolving the conflict between overshoot and speed, reducing external compensation energy, and decreasing drive voltage consumption; 2) They track the variable trends of the hemispherical gyroscope in real time using an extended state observer, resulting in low model dependence; 3) They eliminate noise through a nonlinear state error feedback control law, exhibiting strong anti-interference capabilities and robustness. Furthermore, ADRCs address the issue of achieving good control performance even when the system's dynamic model is unclear and the control gain has significant uncertainties.

Claims

1. A method for identifying errors in an open-loop hemispherical resonant gyroscope, characterized in that, include: Calculate the first-order and second-order nonlinear state errors of the harmonic oscillator amplitude of the gyroscope, respectively; The first response function is determined based on the first-order nonlinear state error; The second response function is determined based on the second-order nonlinear state error; The first coefficient of the first response function and the second coefficient of the second response function are obtained by using the particle swarm optimization algorithm. Finally, the control force of the gyroscope is determined based on the first response function, the second response function, the first coefficient, and the second coefficient. The calculation of the first-order and second-order nonlinear state errors of the gyroscope's harmonic oscillator amplitude includes: The first-order state estimate of the gyroscope's harmonic oscillator amplitude is obtained by weighted calculation using the extended state system based on the extended state error, the third coefficient of the extended state error, the first-order differential of the gyroscope's harmonic oscillator amplitude, and the second-order differential of the harmonic oscillator amplitude. The difference between the first-order state estimate and the first preset state fitting value is calculated to obtain the first-order nonlinear state error. The calculation method for the expansion state error is as follows: The expansion state error is obtained by calculating the difference between the first derivative of the harmonic oscillator amplitude and the preset harmonic oscillator amplitude; The calculation of the first-order and second-order nonlinear state errors of the gyroscope's harmonic oscillator amplitude includes: The second-order state estimate of the gyroscope's harmonic oscillator amplitude is obtained by weighted calculation using the extended state system based on the extended state error, the first extended state response function corresponding to the state error, the fourth coefficient of the first extended state response function, the second derivative of the gyroscope's harmonic oscillator amplitude, and the third derivative of the harmonic oscillator amplitude. The second-order nonlinear state error is obtained by calculating the difference between the second-order state estimate of the harmonic oscillator amplitude and the second preset state fitting value.

2. The method for identifying errors in an open-loop hemispherical resonant gyroscope as described in claim 1, characterized in that, The method for calculating the first-order differential is as follows: The amplitude of the harmonic oscillator of the gyroscope is differentiated by a tracking differentiator to obtain the first derivative of the harmonic oscillator amplitude.

3. The method for identifying errors in an open-loop hemispherical resonant gyroscope as described in claim 1, characterized in that, Determining the first response function based on the first-order nonlinear state error includes: The first-order nonlinear state error is used as the input to a preset step response function to determine the first response function.

4. The method for identifying errors in an open-loop hemispherical resonant gyroscope as described in claim 1, characterized in that, Determining the second response function based on the second-order nonlinear state error includes: The second-order nonlinear state error is used as the input to a preset step response function to determine the second response function.

5. The method for identifying errors in an open-loop hemispherical resonant gyroscope as described in claim 1, characterized in that, The first coefficient of the first response function and the second coefficient of the second response function were obtained by using the particle swarm optimization algorithm.

6. The method for identifying errors in an open-loop hemispherical resonant gyroscope as described in claim 4, characterized in that, Also includes: Calculate the corresponding second expansion state response function based on the expansion state error; The third-order state estimate of the harmonic oscillator amplitude is obtained by weighting the third-order derivative of the gyroscope's harmonic oscillator amplitude and the second extended state response function through the extended state system. Calculate the difference between the control force of the gyroscope and the third-order state estimate; The total disturbance value of the system is obtained by calculating the ratio of the difference to the preset value; The preset perturbation of the extended state system is updated by obtaining the total perturbation.

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